The present study research article proposes a modified test for misspecification of the stochastic linear regression model and a new test for predictive accuracy of stochastic linear regression model. In addition to this modified Lagrange Multiplier (LM) test for misspecification of stochastic linear regression has been developed. In the derivation of the test statistics internally studentized residuals have been used. William A. Branch et.al [1] presented a stochastic non-linear self-referential model in which expectations are based on linear perceptions. I.sh. Torgovitski et.al [2] in this paper discussed the problem of raising the efficiency of the regression coefficients estimation as suggested an approach which allows as to reduce mathematical expectations of the square of deviation of the response prediction.